Defining Polygons Polygon : A plane figure that formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint and no two segments with a common endpoint are collinear. - The segments are called the sides of the polygon, and the common endpoints are called the verticles of the polygon.
Reflection Symmetry
A figure has reflection symmetry if and only if its reflected image across a line coincides exactly with the preimage. The line is called an axis of symmetry.
Triangles Classified by Number of Congruent Sides
Three congruent sides: Equilateral (each angle = 60 degrees)
At least two congruent sides: Isosceles
No congruent sides: Scalene
Isosceles Triangle Diagram
Scalene Rotational Symmetry
A figure has rotational symmetry is and only if has at least one rotation image, not counting rotation images of 0 degrees or multiples of 360 degrees, that coincides with the original image. Equiangular Polygon
All sides are congruent. Regular Polygon
The polygon is both equiangular and equilateral.
Central Angle
Theta = 360/n
Polygon# of sides
Triangle 3
Square 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Hendecagon 11
Dodecagon 12
Tridecagon 13
n-gon n- number of sides
Three congruent sides: equilateral
At least two congruent sides: isosceles
No congruent sides: scalene
Polygon : A plane figure that formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint and no two segments with a common endpoint are collinear.
- The segments are called the sides of the polygon, and the common endpoints are called the verticles of the polygon.
Reflection Symmetry
A figure has reflection symmetry if and only if its reflected image across a line coincides exactly with the preimage. The line is called an axis of symmetry.
Triangles Classified by Number of Congruent Sides
Three congruent sides: Equilateral (each angle = 60 degrees)
At least two congruent sides: Isosceles
No congruent sides: Scalene
Scalene
Rotational Symmetry
A figure has rotational symmetry is and only if has at least one rotation image, not counting rotation images of 0 degrees or multiples of 360 degrees, that coincides with the original image.
Equiangular Polygon
All sides are congruent.
Regular Polygon
The polygon is both equiangular and equilateral.
Central Angle
Theta = 360/n
Polygon # of sides
Triangle 3
Square 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Hendecagon 11
Dodecagon 12
Tridecagon 13
n-gon n- number of sides
Three congruent sides: equilateral
At least two congruent sides: isosceles
No congruent sides: scalene